Is establishing a congregational prayer in mosques on New Year's Eve, under the pretext of opposing the polytheists and shielding people from temptations, considered an innovation (bid'ah)? And does that mean that whenever there is a holiday for the disbelievers, we should initiate an act of worship?

It is not permissible to single out the days of thefar's (disbelievers') festivals for worship, because there is no proof of that from the Prophet, peace and blessings be upon him, and every action not in accordance with the command of the religion is rejected. Furthermore, singling out their festivals for worship carries the risk of people becoming accustomed to them and common folk believing them to be Sunnah (definition), which could lead to an innovation (bid'ah) and might be a form of participating in their glorification of their festivals. Therefore, scholars disliked fasting on their festival days, such as Nowruz and Mehrgan, because that is an imitation of them.